Concentration of Bloch eigenstates in the presence of gauge at the semi-classical limit

Details Concentration of Bloch eigenstates in the presence of gauge at the semi-classical limit Concentration of Bloch eigenstates in the presence of gauge at the semi-classical limit

2009-02-19

arxiv.org/abs/0902.3355v1

Physics

Mathematical Physics

7 pages

Scientific paper

We prove a concentration result of a Bloch eigenstate in a periodic channel under a constant gauge. In the semi-classical limit $h--> 0$ these eigenstates concentrate near a maximizer of the scalar potential of the associated Schrodinger operator, provided the constant gauge converges to a critical value from above. This is in contrast with the ground states which concentrate for any gauge in this limit near a minimizer of the scalar potential.

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